Preheat a panini grill to medium high. Place the doughnuts inside and press for 2 to 3 minutes. (If you don't have a panini grill, you can also use a grill pan and place a weight on top of the doughnuts to press them down.)
Meanwhile, microwave the chocolate-hazelnut spread until melted, about 40 seconds. Serve the doughnuts with the chocolate-hazelnut sauce for dipping.